Please check the ingredients before taking my recommendations. That said , Hoisin sauce is great, duck sauce, sriracha, not a sauce but Chinese 5 spice powder can be used to flavor whatever you are making. You can also build sauces using soy sauce as a base, honey garlic sauce for example. Chinese peanut sauce, satay sauce. I am sure you can find some recipes on FOOD52. I didn't even touch on Korean and Japanese cuisines. So much yu can do, lot's of options out there for you but like I said please check the ingredients on any store bought sauces.

Here is a recipe for Vegan Fish sauce from the Kitchn. I haven't tried it, but I like the ingredients. I make a lot of dashi for hot and sour soup in the winter, so I would use Kombucha for the seaweed, but they use Wakame.

Amazon carries a vegan oyster sauce, but there are recipes for that online as well. Also, check the ingredients on the Golden Mountain Seasoning Sauce. That has a lot of umami flavor, but I haven't looked at the label in a while.

a few suggestions -
1) There are recipes for homemade vegetarian replacement/substitute for fish sauce. If you can't find one, let me know & I'll post one on this site.
2) I think there is now a vegetarian version of Worcestershire sauce, itself a knock-off of Asian fermented fish sauces.
3) For umami flavors, look to fermented tofu or other non-fish foods

Since I'm assuming you looking to make other sauces and marinades; I would use a dark miso paste or black garlic to add the funky and umami notes. You may need to add a teaspoon or few of water (or stock, vinegar, mirin, or any liquid) to get the correct consistency in the final dish.

On black garlic: I totally thought it was just some trendy-fad thing not worth tracking down when I started reading about it everywhere earlier in the year. But then a couple weeks ago there was no good-looking garlic heads at my grocery store but they did have packages of black garlic sitting right there so I picked one up and it is truly as amazing as all of the hype. So sticky and funky and perfect. Given the premises of your question I highly recommend ordering it online if no stores near you carry any.

There are mushroom flavored soy sauces that are very tasty as an alternative to fish sauce, and for oyster sauce I would use Indonesian "Kecap Manis" which is also called sweet soy sauce that is very syrupy and delicious, easily found at an Asian market.

Fish sauce substitute?
Thai light soy sauce. The light body mimics the consistency of fish sauce but it’s a little sweeter and has less of a tendency to overpower what it’s mixed into, like darker soy sauces do. Oh yeah, it’s usually cheaper than fish sauce, too. You can find it easily at Asian markets.

Kombu is a type of kelp (a salt water seaweed) which can (and often does) have traces of fish on it, depending on how it's been processed. Most of the stuff we want from kombu is on the outer layer so getting rid of any fish traces on the outside of the kombu would remove most of the umami benefits. Kombu probably won't cause a reaction unless the person is allergic to traces of fish.

Kombu does serve as fish habitat and draws on the same nutrients. I'm not a marine biologist so I can't say whether or not that might possibly trigger an allergic reaction. But some sea and freshwater vegetation can produce lethal reactions. Apparently there's a type of lily pad that is especially dangerous.

At a large Asian market, I have found "Vegetarien Fish Sauce, Nuoc Mam Am Chay" -- ingredients: Soya Sauce, salt, sugar, water, chili, acid citric, .1% sorbic acid. I can't compare its taste to authentic fish sauce, but it does make a good addition to recipes that call for fish sauce. Reasonable -- 22 fl. oz. for $3.19.
The store also carries a Kikkoman Worcestershire sauce that has no fish or seafood ingredients. Not Bulldog Sauce, which is made with dried sardine extract.
I love kecap manis, but I don't think it gives you the taste of fish sauce.